Movements done in script do not show in game view
There is no bpy module in game (same problem as this one and this one).
You really are moving the cube. Everything you described proves exactly this.
The console output shows the location changing, and when you exit the game the cube is in the new location.
Assuming blender is laid out like you have it in that screen shot. Exit the BGE, then press the &quot;Run Script&quot; button in the text editor. That will run your code, you will see the cube move every time you click the button.
Now how to make it work.
You need to use the bge module.
To move a cube in game like you are doing now would be like this:
import bge, mathutils

# the object holding the logic brick running this script
obj = bge.logic.getCurrentController().owner

obj.worldPosition += mathutils.Vector((1, 1, 1))

Or if you want to get the object by name:
obj = bge.logic.getCurrentScene().objects['Cube']